Numerical solution of linear integral equations system using the Bernstein collocation method

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 6 Absolute errors for Example 3

$t = \frac{1}{2^{r}}$	ANN method			Trapezoidal quadrature rule
$t = \frac{1}{2^{r}}$	$e_{1, 3} (t)$	$e_{2, 3} (t)$	$e_{3, 3} (t)$	$e_{1, 3} (t)$	$e_{2, 3} (t)$	$e_{3, 3} (t)$
r = 1	2.4 × 10⁻²	7.2 × 10⁻³	7.8 × 10⁻⁴	6.2 × 10⁻³	5.8 × 10⁻³	8.1 × 10⁻³
r = 2	6.1 × 10⁻³	4.9 × 10⁻³	5.7 × 10⁻⁴	2.0 × 10⁻²	2.0 × 10⁻²	2.1 × 10⁻²
r = 3	1.3 × 10⁻²	4.4 × 10⁻³	5.1 × 10⁻⁴	3.7 × 10⁻²	2.1 × 10⁻²	2.4 × 10⁻²
r = 4	1.4 × 10⁻²	4.2 × 10⁻³	5.1 × 10⁻⁴	2.8 × 10⁻²	1.5 × 10⁻²	3.2 × 10⁻²
r = 5	1.5 × 10⁻²	4.3 × 10⁻³	5.1 × 10⁻⁴	2.5 × 10⁻³	4.8 × 10⁻³	5.7 × 10⁻³
r = 6	1.6 × 10⁻²	4.2 × 10⁻³	5.1 × 10⁻⁴	2.1 × 10⁻²	5.3 × 10⁻²	6.7 × 10⁻³
r = 7	1.6 × 10⁻²	4.3 × 10⁻³	5.0 × 10⁻⁴	4.7 × 10⁻²	6.9 × 10⁻³	7.3 × 10⁻³
r = 8	1.6 × 10⁻²	4.3 × 10⁻³	5.0 × 10⁻⁴	4.3 × 10⁻²	3.4 × 10⁻²	2.2 × 10⁻²
r = 9	1.6 × 10⁻²	4.3 × 10⁻³	5.1 × 10⁻⁴	2.4 × 10⁻²	3.3 × 10⁻⁴	2.6 × 10⁻²